Enumerative Induction and Lawlikeness

Abstract

The paper is based on ranking theory, a theory of degrees of disbelief (and hence belief). On this basis, it explains enumerative induction, the confirmation of a law by its positive instances, which may, indeed, take various schemes. It gives a ranking theoretic explication of a possible law or a nomological hypothesis. It proves, then, that such schemes of enumerative induction uniquely correspond to mixtures of such nomological hypotheses. Thus, it shows both that de Finetti's probabilistic representation theorems may be transformed into an account of confirmation of possible laws and that enumerative induction is equivalent to such an account. The paper concludes with some remarks about the apriority of lawfulness, or the uniformity of nature.